On The Continuous Series for $${{\widehat{sl(2,{\mathbb{R}})}}}$$ s l ( 2 , R ) ^

Abstract

We construct the representations of affine sl(2,R) starting from the unitary representations of the loop ax+b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the appearing divergencies. We view our construction as a step towards a realization of the principal series representations of affine sl(2,R).